Contact Thermal#
Contact thermal transfer exchanges heat between the surfaces of two discrete elements or blocks in contact. It provides a thermal connection across a mechanical contact and is commonly modeled with a conductance proportional to the temperature difference across the interface.
Interface law#
Let \(\Gamma_c\) denote the active contact interface, and let \(T_t\) and \(T_c\) be the temperatures on the target and contactor sides. The normal heat flux from target to contactor is
where \(h_c\) is the thermal contact conductance. The heat-transfer rate over the interface is
For a uniform conductance and temperature difference over an interface of area \(A_c\), this reduces to \(\dot Q_{t\rightarrow c}=h_cA_c(T_t-T_c)\). In a two-dimensional model, the measure \(\mathrm{d}\Gamma\) is a boundary length and the out-of-plane thickness must be included if a three-dimensional heat rate is required.
Energy conservation and interpretation#
The equal-and-opposite heat rate is applied to the other body:
Thus, contact exchange redistributes energy between the bodies but does not create or remove energy from the pair. If \(T_t>T_c\) and \(h_c>0\), heat flows from the target to the contactor. A larger conductance approaches the perfect-contact limit, while a small conductance represents a more thermally resistive interface. The conductance may be prescribed or calibrated as an effective parameter; its dependence on contact pressure, roughness, aperture, and interface material is model-specific.
Contact thermal transfer applies only where a contact interface is defined. Heat transfer across an open fracture or a gap requires a fracture-resistance or other gap-transfer model. Care is needed to avoid applying both laws to the same interface unless their resistances have been intentionally combined.